Advertisements
Advertisements
Question
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 34x − 22x3 − 12x4 − 10x2 − 75 | 3x + 7 |
Advertisements
Solution
Quotient = - 4x3 + 2x2 - 8x + 30
Remainder = - 285
Divisor = 3x + 7
Divisor x Quotient + Remainder = (3x + 7) (- 4x3 + 2x2 - 8x + 30) - 285
= 12x4 + 6x3 - 24x2 + 90x - 28x3 + 14x2 - 56x + 210 - 285
= - 12x 4 - 22x3 -10x2 + 34x - 75
= Dividend
Thus,
Divisor x Quotient + Remainder = Dividend
Hence verified.
RELATED QUESTIONS
Divide the given polynomial by the given monomial.
(x3 + 2x2 + 3x) ÷ 2x
Write each of the following polynomials in the standard form. Also, write their degree.
Divide 6x3y2z2 by 3x2yz.
Divide −21abc2 by 7abc.
Divide 4y2 + 3y +\[\frac{1}{2}\] by 2y + 1.
Divide 14x2 − 53x + 45 by 7x − 9.
Divide 3y4 − 3y3 − 4y2 − 4y by y2 − 2y.
Using division of polynomials, state whether
z2 + 3 is a factor of z5 − 9z
Divide 27y3 by 3y
The denominator of a fraction exceeds Its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, we get `3/2`. Find the original fraction.
